exact category

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• Exact category — In mathematics, an exact category is a concept of category theory due to Daniel Quillen which is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and… …   Wikipedia

• Category management — is a retailing concept in which the total range of products sold by a retailer is broken down into discrete groups of similar or related products; these groups are known as product categories. Examples of grocery categories may be : tinned fish,… …   Wikipedia

• Exact functor — In homological algebra, an exact functor is a functor, from some category to another, which preserves exact sequences. Exact functors are very convenient in algebraic calculations, roughly speaking because they can be applied to presentations of… …   Wikipedia

• Exact sequence — In mathematics, especially in homological algebra and other applications of abelian category theory, as well as in differential geometry and group theory, an exact sequence is a (finite or infinite) sequence of objects and morphisms between them… …   Wikipedia

• Category:Date of death unknown — This category is not shown on its member pages, unless the appropriate user preference is set. This category (and similarly Category:Date of birth unknown) is intended for articles about people, mainly historical, whose year of death is known,… …   Wikipedia

• Category of groups — In mathematics, the category Grp has the class of all groups for objects and group homomorphisms for morphisms. As such, it is a concrete category. The study of this category is known as group theory.The monomorphisms in Grp are precisely the… …   Wikipedia

• Category of abelian groups — In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category.The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the… …   Wikipedia

• Derived category — In mathematics, the derived category D(C) of an abelian category C is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on C. The construction proceeds on the… …   Wikipedia

• Waldhausen category — In mathematics a Waldhausen category is a category C equipped with cofibrations co( C ) and weak equivalences we( C ), both containing all isomorphisms, both compatible with pushout, and co( C ) containing the unique morphisms :scriptstyle 0,… …   Wikipedia

• Regular category — In category theory, a regular category is a category with finite limits and coequalizers of kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence …   Wikipedia

• Abelian category — In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototype example of an abelian category is the category of… …   Wikipedia